Question: A website offers a coupon such that each customer has a $15\%$ chance of getting the coupon each day they visit the site. Aya visits the website for $6$ consecutive days. What is the probability that at Aya will be offered a coupon on at least one of the days she visits the website? Round your answer to the nearest hundredth. $P(\text{at least one coupon})=$
Strategy In this situation it is much easier to calculate the probability of the event we are looking for (at least one day with a coupon) by calculating the probability of its complement (all days without a coupon), and subtracting from $1$. In other words, we can use this strategy: $P(\text{at least one coupon})=1-P(\text{no coupon all 6 days})$ Calculations $\begin{aligned} &\phantom{=}P(\text{at least one coupon}) \\\\ &=1-P(\text{no coupon all 6 days}) \\ \\ &=1-0.85^{6} \\ \\ &\approx 1-0.377 \\ \\ &\approx 0.623\end{aligned}$ Answer $P(\text{at least one coupon}) \approx 0.62$